Two racing cars `'A'` and `'B'` having masses `'M'` and `'2m'` respectively start running from the starting line on a horizontal plane.Both cars `'A'` and `B'` have same speed `'V'` which is constant through out the journey. The track of the two cars are the arcs of concentric circle having centres `O_(1)` and `O_(2)` as shwon in figure with data. The friction coefficient of the two cars with the road is same. There is a finishing line at the end of the arc. Using these informations solve the following questions.

The magnitude of relative acceleration of two cars when car `'A'` just reaches the end of circular arc of radius `Y`.

Options

A. 0
B. `(sqrt(5-2))(V^(2))/(2r)`
C. `sqrt(2)(V^(2))/(r)`
D. `(V^(2))/(r)`

Answer

B

Explanation

For `A` ,
For `B` ,
`=a_(rel)={((v^(2))/(r)-(v^(2))/(2sqrt(2)r))hat(i)-(v^(2))/(2sqrt(2)e)hat(j)}`
`|a_(rel)|=(v^(2))/(2sqrt(2)r)[(2sqrt(2)-1)^(2)+1^(2)]`
`=(v^(2))/(2r)sqrt((8+1-4sqrt(2)+1)/(2))`
`=(v^(2))/(2r)sqrt((10-4sqrt(2))/(2))=(v^(2))/(2r)sqrt((5-2sqrt(2)))`
`=(v^(2))/(2r)sqrt(2.172)(B)`